### Decimal Fraction

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__Fraction__

Fraction

1.

Ex :

A fraction has two parts,

2.Type of Fractions

3. Annexing Zeros to the extreme right of a decimal fraction

Annexing zeros to the extreme right of a decimal fraction does not change its value.

Examples

0.4 = 0.40 = 0.400 = 0.4000, etc.

1.21 = 1.210 = 1.2100 = 1.21000, etc

4. Some Basic Formulae:

__Definition__: A fraction is an expression that indicates the quotient of two quantities.Ex :

2

1

,
3

1

,
5

6

,
- 5

8

.
A fraction has two parts,

**Numerator and Denominator**. Numerator is the number at the top of the fraction and denominator is the number at the bottom of the fraction.2.Type of Fractions

i. Common Fraction : A common fraction (also known as Vulgar fraction and simple fraction) is a fraction in which both numerator and denominator are integers (As with other fractions, the denominator cannot be zero)

ii. A decimal fraction is a fraction in which denominator is an integer power of ten. (The term decimals are commonly used to refer decimal fractions).

3

2

,
12

7

,
- 3

2

,
ii. A decimal fraction is a fraction in which denominator is an integer power of ten. (The term decimals are commonly used to refer decimal fractions).

10

1

= 0.1 100

1

= 0.01 100

17

= 0.17 3. Annexing Zeros to the extreme right of a decimal fraction

Annexing zeros to the extreme right of a decimal fraction does not change its value.

Examples

0.4 = 0.40 = 0.400 = 0.4000, etc.

1.21 = 1.210 = 1.2100 = 1.21000, etc

4. Some Basic Formulae:

(a + b)(a - b) = (a

(a + b)

(a - b)

(a + b + c)

(a

(a

(a

When a + b + c = 0, then a

^{2}- b^{2})(a + b)

^{2}= (a^{2}+ b^{2}+ 2ab)(a - b)

^{2}= (a^{2}+ b^{2}- 2ab)(a + b + c)

^{2}= a^{2}+ b^{2}+ c^{2}+ 2(ab + bc + ca)(a

^{3}+ b^{3}) = (a + b)(a^{2}- ab + b^{2})(a

^{3}- b^{3}) = (a - b)(a^{2}+ ab + b^{2})(a

^{3}+ b^{3}+ c^{3}- 3abc) = (a + b + c)(a^{2}+ b^{2}+ c^{2}- ab - bc - ac)When a + b + c = 0, then a

^{3}+ b^{3}+ c^{3}= 3abc.